Pessimistic evasive flow capturing problems

Abstract

The evasive flow capturing problem (EFCP) is to locate a set of law enforcement facilities to intercept unlawful flows. One application of the EFCP is the location problem of weigh-in-motion systems deployed by authorities to detect overloaded vehicles characterized by evasive behavior. In contrast to the existing literature, this study focuses on the bounded-rationality of drivers and represents the most generic form of the EFCP. We present two pessimistic formulations of the problem to capture various degrees of ambiguity in the route choice of drivers. In particular, we look at the worst-case scenario, when drivers select roads with the highest damage costs. The resulting formulations yield a robust network design and represent the realistic behavior of drivers. The pessimistic formulations introduce another level in the optimization problem, for which we propose a cutting plane algorithm. The proposed solution methods demonstrate their effectiveness on real and randomly generated networks. We also provide numerical analysis to measure the value of considering pessimistic formulations and demonstrate the vulnerability of optimizing and optimistic assumptions on the behavior of drivers.